Translations of Mathematical Monographs 1999; 332 pp; hardcover Volume: 181 ISBN10: 0821805320 ISBN13: 9780821805329 List Price: US$129 Member Price: US$103.20 Order Code: MMONO/181
 This book places character theory and its applications to finite groups within the reach of people with a comparatively modest mathematical background. The work concentrates mostly on applications of character theory to finite groups. The main themes are degrees and kernels of irreducible characters, the class number and the number of nonlinear irreducible characters, values of irreducible characters, characterizations and generalizations of Frobenius groups, and generalizations of monomial groups. The presentation is detailed, and many proofs of known results are new. Readership Graduate students and research mathematicians working in finite group theory and applications. Reviews "The reviewer regards the book as a "must", certainly due to the techniques and results offered, it is up to date, and it is ... a very welcome and illuminating contribution in presenting to the mathematical community the beauty of the theory of characters of finite groups."  Zentralblatt MATH Table of Contents  Degrees and kernels of irreducible characters
 Involutions
 Connectedness and Zassenhaus groups
 The Nagao theorem
 Linear groups
 Permutation characters
 Characters of SL\((2,p^n)\)
 Zeros of characters
 The Schur index
 On degrees of irreducible components of induced characters
 Groups in which only two nonlinear irreducible characters have equal degrees
 Groups with small sums of degrees of some characters
 On sums of degrees of irreducible characters
 Groups whose nonlinear irreducible characters take three distinct values
 Nonsolvable groups with many involutions
 On kernels of nonlinear irreducible characters
 On monolithic characters
 The class number
 Problems
 Notes on the bibliography
 Bibliography
 Author index
 Subject index
 List of corrections to part 1
